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<br />,4 <br /> <br />TECHNIQUES OF WATER-RESOURCES lNVESTIGATIONS <br /> <br /> <br />10 <br /> <br /> I, T <br /> 8 ~--- <br />>- <br />'" Critical-flow section <br />'" <br />"- <br />~ 6 <br />-' <br />~ <br />J: <br />>- <br />.. <br />'" <br />" <br />:;; 4 <br />::J <br />:;; <br />X <br />'" <br />:;; <br /> 2 <br /> de <br /> <br />-1- <br /> <br />Q =a constant <br /> <br />: <br />TranQuil flow and mild slopes <br /> <br />1 <br />Rapid flow and steep Slopes <br /> <br />00 <br /> <br />2 <br /> <br />4 6 <br />SPECIFIC ENERGY (Ho = d + <br /> <br />8 <br />V 2 <br />-" I. IN FEET <br />29 <br /> <br />10 <br /> <br />12 <br /> <br />Figure 3.-Relation betwe1i!" specific energy and depth. <br /> <br />For the condition of minimum specific energy <br />and critical depth, the discharge equation for a <br />section of any shape can be written <br /> <br />d,=maximum depth of water in the eriti- <br />cal-flo"\I~ section, and <br />D=inside diameter of circular section, <br /> <br />Q=A:"# <br /> <br />(1) <br /> <br />The two types of flow in this classification are <br />1 and 2, <br /> <br />or <br /> <br />Type 1 flow <br /> <br />In type 1 flow, as illustrated on figure 2, the <br />water passes through critical depth near the <br />culvert entrance. The headwater-diameter ratio, <br />(h,-z)/D, is limited to a maximum of 1.5 and <br />the culvert barrel flows partly full. The slope <br />of the culvert barrel, So> must be greater than <br />the critical slope, S" and the tailwater elevation, <br />h" must be less than the elevation of the water <br />surface at the control section, h., <br />The discharge equation is <br /> <br />Q=CA,.J29 (h,-z+ "I;' ~ -~,-h~l:~} (5) <br />g <br /> <br />Q=A,{!j(l;" <br /> <br />(2) <br /> <br />The discharge equation can be simplified <br />according to the shape of the sections. Thus, <br />for rectangular sections, <br /> <br />Q=5.67bd:I', <br /> <br />(3) <br /> <br />and for circular sections, <br /> <br />Q=C,D'I', <br /> <br />(4) <br /> <br />where <br /> <br />b=width of section, <br />C,=function of d,/D, <br /> <br />e <br /> <br />. <br /> <br />e <br /> <br />, <br /> <br />-e <br />